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A086759
Permanent of the Cayley addition table of Z_{n}. a(n) is the permanent of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1.
2
0, 1, 9, 164, 5050, 227508, 14064519, 1146668608, 119249333028, 15400125776000, 2417814003691405, 453536611741073664, 100178077459552487070, 25735749696251388478720, 7608415981499790110521875, 2564724413131659780025106432, 977834710569917222742633274504
OFFSET
1,3
LINKS
Robert Connelly, Maurice Pierre, Maximally Dense Disc Packings on the Plane, arXiv:1907.03652 [math.MG], 2019.
EXAMPLE
a(9) is the permanent of the matrix
0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 0
2 3 4 5 6 7 8 0 1
3 4 5 6 7 8 0 1 2
4 5 6 7 8 0 1 2 3
5 6 7 8 0 1 2 3 4
6 7 8 0 1 2 3 4 5
7 8 0 1 2 3 4 5 6
8 0 1 2 3 4 5 6 7
MATHEMATICA
Array[With[{s = Range[0, #]}, Permanent@ Array[RotateLeft[s, #] &, Last@ s + 1, 0]] &, 16, 0] (* Michael De Vlieger, Sep 03 2019 *)
PROG
(PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p) for(n=1, 21, a=matrix(n, n, i, j, ((i+j-2)%n)); print1(permRWNb(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
(PARI) a(n) = matpermanent(matrix(n, n, i, j, (i+j-2) % n)) \\ Stefano Spezia, Oct 25 2020
CROSSREFS
Sequence in context: A354900 A354892 A377329 * A053130 A219074 A166180
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 01 2003
EXTENSIONS
a(9) from Neven Juric (neven.juric(AT)apis-it.hr), Jul 11 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
a(17) from Michael De Vlieger, Sep 03 2019
STATUS
approved